/*	$NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $	*/
/*	$OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $	*/
/* $FreeBSD$ */

/*-
 * Copyright 2002 Niels Provos <provos@citi.umich.edu>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#ifndef _SYS_TREE_H_
#define _SYS_TREE_H_

#ifdef __cplusplus
extern "C"
{
#endif

#include "../ext4_config.h"

	/*
	 * This file defines data structures for different types of trees:
	 * splay trees and red-black trees.
	 *
	 * A splay tree is a self-organizing data structure.  Every operation
	 * on the tree causes a splay to happen.  The splay moves the requested
	 * node to the root of the tree and partly rebalances it.
	 *
	 * This has the benefit that request locality causes faster lookups as
	 * the requested nodes move to the top of the tree.  On the other hand,
	 * every lookup causes memory writes.
	 *
	 * The Balance Theorem bounds the total access time for m operations
	 * and n inserts on an initially empty tree as O((m + n)lg n).  The
	 * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
	 *
	 * A red-black tree is a binary search tree with the node color as an
	 * extra attribute.  It fulfills a set of conditions:
	 *	- every search path from the root to a leaf consists of the
	 *	  same number of black nodes,
	 *	- each red node (except for the root) has a black parent,
	 *	- each leaf node is black.
	 *
	 * Every operation on a red-black tree is bounded as O(lg n).
	 * The maximum height of a red-black tree is 2lg (n+1).
	 */

#define SPLAY_HEAD(name, type)                        \
	struct name                                       \
	{                                                 \
		struct type *sph_root; /* root of the tree */ \
	}

#define SPLAY_INITIALIZER(root) \
	{NULL}

#define SPLAY_INIT(root)         \
	do                           \
	{                            \
		(root)->sph_root = NULL; \
	} while (/*CONSTCOND*/ 0)

#define SPLAY_ENTRY(type)                           \
	struct                                          \
	{                                               \
		struct type *spe_left;	/* left element */  \
		struct type *spe_right; /* right element */ \
	}

#define SPLAY_LEFT(elm, field) (elm)->field.spe_left
#define SPLAY_RIGHT(elm, field) (elm)->field.spe_right
#define SPLAY_ROOT(head) (head)->sph_root
#define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == NULL)

/* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
#define SPLAY_ROTATE_RIGHT(head, tmp, field)                           \
	do                                                                 \
	{                                                                  \
		SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \
		SPLAY_RIGHT(tmp, field) = (head)->sph_root;                    \
		(head)->sph_root = tmp;                                        \
	} while (/*CONSTCOND*/ 0)

#define SPLAY_ROTATE_LEFT(head, tmp, field)                            \
	do                                                                 \
	{                                                                  \
		SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \
		SPLAY_LEFT(tmp, field) = (head)->sph_root;                     \
		(head)->sph_root = tmp;                                        \
	} while (/*CONSTCOND*/ 0)

#define SPLAY_LINKLEFT(head, tmp, field)                        \
	do                                                          \
	{                                                           \
		SPLAY_LEFT(tmp, field) = (head)->sph_root;              \
		tmp = (head)->sph_root;                                 \
		(head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \
	} while (/*CONSTCOND*/ 0)

#define SPLAY_LINKRIGHT(head, tmp, field)                        \
	do                                                           \
	{                                                            \
		SPLAY_RIGHT(tmp, field) = (head)->sph_root;              \
		tmp = (head)->sph_root;                                  \
		(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \
	} while (/*CONSTCOND*/ 0)

#define SPLAY_ASSEMBLE(head, node, left, right, field)                   \
	do                                                                   \
	{                                                                    \
		SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);  \
		SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field); \
		SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);  \
		SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);  \
	} while (/*CONSTCOND*/ 0)

	/* Generates prototypes and inline functions */

#define SPLAY_PROTOTYPE(name, type, field, cmp)                     \
	void name##_SPLAY(struct name *, struct type *);                \
	void name##_SPLAY_MINMAX(struct name *, int);                   \
	struct type *name##_SPLAY_INSERT(struct name *, struct type *); \
	struct type *name##_SPLAY_REMOVE(struct name *, struct type *); \
                                                                    \
	/* Finds the node with the same key as elm */                   \
	static __inline struct type *                                   \
	name##_SPLAY_FIND(struct name *head, struct type *elm)          \
	{                                                               \
		if (SPLAY_EMPTY(head))                                      \
			return (NULL);                                          \
		name##_SPLAY(head, elm);                                    \
		if ((cmp)(elm, (head)->sph_root) == 0)                      \
			return (head->sph_root);                                \
		return (NULL);                                              \
	}                                                               \
                                                                    \
	static __inline struct type *                                   \
	name##_SPLAY_NEXT(struct name *head, struct type *elm)          \
	{                                                               \
		name##_SPLAY(head, elm);                                    \
		if (SPLAY_RIGHT(elm, field) != NULL)                        \
		{                                                           \
			elm = SPLAY_RIGHT(elm, field);                          \
			while (SPLAY_LEFT(elm, field) != NULL)                  \
			{                                                       \
				elm = SPLAY_LEFT(elm, field);                       \
			}                                                       \
		}                                                           \
		else                                                        \
			elm = NULL;                                             \
		return (elm);                                               \
	}                                                               \
                                                                    \
	static __inline struct type *                                   \
	name##_SPLAY_MIN_MAX(struct name *head, int val)                \
	{                                                               \
		name##_SPLAY_MINMAX(head, val);                             \
		return (SPLAY_ROOT(head));                                  \
	}

/* Main splay operation.
 * Moves node close to the key of elm to top
 */
#define SPLAY_GENERATE(name, type, field, cmp)                                  \
	struct type *                                                               \
	name##_SPLAY_INSERT(struct name *head, struct type *elm)                    \
	{                                                                           \
		if (SPLAY_EMPTY(head))                                                  \
		{                                                                       \
			SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;            \
		}                                                                       \
		else                                                                    \
		{                                                                       \
			int __comp;                                                         \
			name##_SPLAY(head, elm);                                            \
			__comp = (cmp)(elm, (head)->sph_root);                              \
			if (__comp < 0)                                                     \
			{                                                                   \
				SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);   \
				SPLAY_RIGHT(elm, field) = (head)->sph_root;                     \
				SPLAY_LEFT((head)->sph_root, field) = NULL;                     \
			}                                                                   \
			else if (__comp > 0)                                                \
			{                                                                   \
				SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field); \
				SPLAY_LEFT(elm, field) = (head)->sph_root;                      \
				SPLAY_RIGHT((head)->sph_root, field) = NULL;                    \
			}                                                                   \
			else                                                                \
				return ((head)->sph_root);                                      \
		}                                                                       \
		(head)->sph_root = (elm);                                               \
		return (NULL);                                                          \
	}                                                                           \
                                                                                \
	struct type *                                                               \
	name##_SPLAY_REMOVE(struct name *head, struct type *elm)                    \
	{                                                                           \
		struct type *__tmp;                                                     \
		if (SPLAY_EMPTY(head))                                                  \
			return (NULL);                                                      \
		name##_SPLAY(head, elm);                                                \
		if ((cmp)(elm, (head)->sph_root) == 0)                                  \
		{                                                                       \
			if (SPLAY_LEFT((head)->sph_root, field) == NULL)                    \
			{                                                                   \
				(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);        \
			}                                                                   \
			else                                                                \
			{                                                                   \
				__tmp = SPLAY_RIGHT((head)->sph_root, field);                   \
				(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);         \
				name##_SPLAY(head, elm);                                        \
				SPLAY_RIGHT((head)->sph_root, field) = __tmp;                   \
			}                                                                   \
			return (elm);                                                       \
		}                                                                       \
		return (NULL);                                                          \
	}                                                                           \
                                                                                \
	void                                                                        \
	name##_SPLAY(struct name *head, struct type *elm)                           \
	{                                                                           \
		struct type __node, *__left, *__right, *__tmp;                          \
		int __comp;                                                             \
                                                                                \
		SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;        \
		__left = __right = &__node;                                             \
                                                                                \
		while ((__comp = (cmp)(elm, (head)->sph_root)) != 0)                    \
		{                                                                       \
			if (__comp < 0)                                                     \
			{                                                                   \
				__tmp = SPLAY_LEFT((head)->sph_root, field);                    \
				if (__tmp == NULL)                                              \
					break;                                                      \
				if ((cmp)(elm, __tmp) < 0)                                      \
				{                                                               \
					SPLAY_ROTATE_RIGHT(head, __tmp, field);                     \
					if (SPLAY_LEFT((head)->sph_root, field) == NULL)            \
						break;                                                  \
				}                                                               \
				SPLAY_LINKLEFT(head, __right, field);                           \
			}                                                                   \
			else if (__comp > 0)                                                \
			{                                                                   \
				__tmp = SPLAY_RIGHT((head)->sph_root, field);                   \
				if (__tmp == NULL)                                              \
					break;                                                      \
				if ((cmp)(elm, __tmp) > 0)                                      \
				{                                                               \
					SPLAY_ROTATE_LEFT(head, __tmp, field);                      \
					if (SPLAY_RIGHT((head)->sph_root, field) == NULL)           \
						break;                                                  \
				}                                                               \
				SPLAY_LINKRIGHT(head, __left, field);                           \
			}                                                                   \
		}                                                                       \
		SPLAY_ASSEMBLE(head, &__node, __left, __right, field);                  \
	}                                                                           \
                                                                                \
	/* Splay with either the minimum or the maximum element                     \
	 * Used to find minimum or maximum element in tree.                         \
	 */                                                                         \
	void name##_SPLAY_MINMAX(struct name *head, int __comp)                     \
	{                                                                           \
		struct type __node, *__left, *__right, *__tmp;                          \
                                                                                \
		SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;        \
		__left = __right = &__node;                                             \
                                                                                \
		while (1)                                                               \
		{                                                                       \
			if (__comp < 0)                                                     \
			{                                                                   \
				__tmp = SPLAY_LEFT((head)->sph_root, field);                    \
				if (__tmp == NULL)                                              \
					break;                                                      \
				if (__comp < 0)                                                 \
				{                                                               \
					SPLAY_ROTATE_RIGHT(head, __tmp, field);                     \
					if (SPLAY_LEFT((head)->sph_root, field) == NULL)            \
						break;                                                  \
				}                                                               \
				SPLAY_LINKLEFT(head, __right, field);                           \
			}                                                                   \
			else if (__comp > 0)                                                \
			{                                                                   \
				__tmp = SPLAY_RIGHT((head)->sph_root, field);                   \
				if (__tmp == NULL)                                              \
					break;                                                      \
				if (__comp > 0)                                                 \
				{                                                               \
					SPLAY_ROTATE_LEFT(head, __tmp, field);                      \
					if (SPLAY_RIGHT((head)->sph_root, field) == NULL)           \
						break;                                                  \
				}                                                               \
				SPLAY_LINKRIGHT(head, __left, field);                           \
			}                                                                   \
		}                                                                       \
		SPLAY_ASSEMBLE(head, &__node, __left, __right, field);                  \
	}

#define SPLAY_NEGINF -1
#define SPLAY_INF 1

#define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y)
#define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y)
#define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y)
#define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y)
#define SPLAY_MIN(name, x) (SPLAY_EMPTY(x) ? NULL \
										   : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
#define SPLAY_MAX(name, x) (SPLAY_EMPTY(x) ? NULL \
										   : name##_SPLAY_MIN_MAX(x, SPLAY_INF))

#define SPLAY_FOREACH(x, name, head)  \
	for ((x) = SPLAY_MIN(name, head); \
		 (x) != NULL;                 \
		 (x) = SPLAY_NEXT(name, head, x))

/* Macros that define a red-black tree */
#define RB_HEAD(name, type)                           \
	struct name                                       \
	{                                                 \
		struct type *rbh_root; /* root of the tree */ \
	}

#define RB_INITIALIZER(root) \
	{NULL}

#define RB_INIT(root)            \
	do                           \
	{                            \
		(root)->rbh_root = NULL; \
	} while (/*CONSTCOND*/ 0)

#define RB_BLACK 0
#define RB_RED 1
#define RB_ENTRY(type)                                \
	struct                                            \
	{                                                 \
		struct type *rbe_left;	 /* left element */   \
		struct type *rbe_right;	 /* right element */  \
		struct type *rbe_parent; /* parent element */ \
		int rbe_color;			 /* node color */     \
	}

#define RB_LEFT(elm, field) (elm)->field.rbe_left
#define RB_RIGHT(elm, field) (elm)->field.rbe_right
#define RB_PARENT(elm, field) (elm)->field.rbe_parent
#define RB_COLOR(elm, field) (elm)->field.rbe_color
#define RB_ROOT(head) (head)->rbh_root
#define RB_EMPTY(head) (RB_ROOT(head) == NULL)

#define RB_SET(elm, parent, field)                         \
	do                                                     \
	{                                                      \
		RB_PARENT(elm, field) = parent;                    \
		RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \
		RB_COLOR(elm, field) = RB_RED;                     \
	} while (/*CONSTCOND*/ 0)

#define RB_SET_BLACKRED(black, red, field) \
	do                                     \
	{                                      \
		RB_COLOR(black, field) = RB_BLACK; \
		RB_COLOR(red, field) = RB_RED;     \
	} while (/*CONSTCOND*/ 0)

#ifndef RB_AUGMENT
#define RB_AUGMENT(x) \
	do                \
	{                 \
	} while (0)
#endif

#define RB_ROTATE_LEFT(head, elm, tmp, field)                        \
	do                                                               \
	{                                                                \
		(tmp) = RB_RIGHT(elm, field);                                \
		if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL)    \
		{                                                            \
			RB_PARENT(RB_LEFT(tmp, field), field) = (elm);           \
		}                                                            \
		RB_AUGMENT(elm);                                             \
		if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) \
		{                                                            \
			if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))      \
				RB_LEFT(RB_PARENT(elm, field), field) = (tmp);       \
			else                                                     \
				RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);      \
		}                                                            \
		else                                                         \
			(head)->rbh_root = (tmp);                                \
		RB_LEFT(tmp, field) = (elm);                                 \
		RB_PARENT(elm, field) = (tmp);                               \
		RB_AUGMENT(tmp);                                             \
		if ((RB_PARENT(tmp, field)))                                 \
			RB_AUGMENT(RB_PARENT(tmp, field));                       \
	} while (/*CONSTCOND*/ 0)

#define RB_ROTATE_RIGHT(head, elm, tmp, field)                       \
	do                                                               \
	{                                                                \
		(tmp) = RB_LEFT(elm, field);                                 \
		if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL)    \
		{                                                            \
			RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);          \
		}                                                            \
		RB_AUGMENT(elm);                                             \
		if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) \
		{                                                            \
			if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))      \
				RB_LEFT(RB_PARENT(elm, field), field) = (tmp);       \
			else                                                     \
				RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);      \
		}                                                            \
		else                                                         \
			(head)->rbh_root = (tmp);                                \
		RB_RIGHT(tmp, field) = (elm);                                \
		RB_PARENT(elm, field) = (tmp);                               \
		RB_AUGMENT(tmp);                                             \
		if ((RB_PARENT(tmp, field)))                                 \
			RB_AUGMENT(RB_PARENT(tmp, field));                       \
	} while (/*CONSTCOND*/ 0)

/* Generates prototypes and inline functions */
#define RB_PROTOTYPE(name, type, field, cmp) \
	RB_PROTOTYPE_INTERNAL(name, type, field, cmp, )
#define RB_PROTOTYPE_STATIC(name, type, field, cmp) \
	RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static)
#define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr) \
	RB_PROTOTYPE_INSERT_COLOR(name, type, attr);            \
	RB_PROTOTYPE_REMOVE_COLOR(name, type, attr);            \
	RB_PROTOTYPE_INSERT(name, type, attr);                  \
	RB_PROTOTYPE_REMOVE(name, type, attr);                  \
	RB_PROTOTYPE_FIND(name, type, attr);                    \
	RB_PROTOTYPE_NFIND(name, type, attr);                   \
	RB_PROTOTYPE_NEXT(name, type, attr);                    \
	RB_PROTOTYPE_PREV(name, type, attr);                    \
	RB_PROTOTYPE_MINMAX(name, type, attr);
#define RB_PROTOTYPE_INSERT_COLOR(name, type, attr) \
	attr void name##_RB_INSERT_COLOR(struct name *, struct type *)
#define RB_PROTOTYPE_REMOVE_COLOR(name, type, attr) \
	attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *)
#define RB_PROTOTYPE_REMOVE(name, type, attr) \
	attr struct type *name##_RB_REMOVE(struct name *, struct type *)
#define RB_PROTOTYPE_INSERT(name, type, attr) \
	attr struct type *name##_RB_INSERT(struct name *, struct type *)
#define RB_PROTOTYPE_FIND(name, type, attr) \
	attr struct type *name##_RB_FIND(struct name *, struct type *)
#define RB_PROTOTYPE_NFIND(name, type, attr) \
	attr struct type *name##_RB_NFIND(struct name *, struct type *)
#define RB_PROTOTYPE_NEXT(name, type, attr) \
	attr struct type *name##_RB_NEXT(struct type *)
#define RB_PROTOTYPE_PREV(name, type, attr) \
	attr struct type *name##_RB_PREV(struct type *)
#define RB_PROTOTYPE_MINMAX(name, type, attr) \
	attr struct type *name##_RB_MINMAX(struct name *, int)

/* Main rb operation.
 * Moves node close to the key of elm to top
 */
#define RB_GENERATE(name, type, field, cmp) \
	RB_GENERATE_INTERNAL(name, type, field, cmp, )
#define RB_GENERATE_STATIC(name, type, field, cmp) \
	RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
#define RB_GENERATE_INTERNAL(name, type, field, cmp, attr) \
	RB_GENERATE_INSERT_COLOR(name, type, field, attr)      \
	RB_GENERATE_REMOVE_COLOR(name, type, field, attr)      \
	RB_GENERATE_INSERT(name, type, field, cmp, attr)       \
	RB_GENERATE_REMOVE(name, type, field, attr)            \
	RB_GENERATE_FIND(name, type, field, cmp, attr)         \
	RB_GENERATE_NFIND(name, type, field, cmp, attr)        \
	RB_GENERATE_NEXT(name, type, field, attr)              \
	RB_GENERATE_PREV(name, type, field, attr)              \
	RB_GENERATE_MINMAX(name, type, field, attr)

#define RB_GENERATE_INSERT_COLOR(name, type, field, attr)       \
	attr void                                                   \
	name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \
	{                                                           \
		struct type *parent, *gparent, *tmp;                    \
		while ((parent = RB_PARENT(elm, field)) != NULL &&      \
			   RB_COLOR(parent, field) == RB_RED)               \
		{                                                       \
			gparent = RB_PARENT(parent, field);                 \
			if (parent == RB_LEFT(gparent, field))              \
			{                                                   \
				tmp = RB_RIGHT(gparent, field);                 \
				if (tmp && RB_COLOR(tmp, field) == RB_RED)      \
				{                                               \
					RB_COLOR(tmp, field) = RB_BLACK;            \
					RB_SET_BLACKRED(parent, gparent, field);    \
					elm = gparent;                              \
					continue;                                   \
				}                                               \
				if (RB_RIGHT(parent, field) == elm)             \
				{                                               \
					RB_ROTATE_LEFT(head, parent, tmp, field);   \
					tmp = parent;                               \
					parent = elm;                               \
					elm = tmp;                                  \
				}                                               \
				RB_SET_BLACKRED(parent, gparent, field);        \
				RB_ROTATE_RIGHT(head, gparent, tmp, field);     \
			}                                                   \
			else                                                \
			{                                                   \
				tmp = RB_LEFT(gparent, field);                  \
				if (tmp && RB_COLOR(tmp, field) == RB_RED)      \
				{                                               \
					RB_COLOR(tmp, field) = RB_BLACK;            \
					RB_SET_BLACKRED(parent, gparent, field);    \
					elm = gparent;                              \
					continue;                                   \
				}                                               \
				if (RB_LEFT(parent, field) == elm)              \
				{                                               \
					RB_ROTATE_RIGHT(head, parent, tmp, field);  \
					tmp = parent;                               \
					parent = elm;                               \
					elm = tmp;                                  \
				}                                               \
				RB_SET_BLACKRED(parent, gparent, field);        \
				RB_ROTATE_LEFT(head, gparent, tmp, field);      \
			}                                                   \
		}                                                       \
		RB_COLOR(head->rbh_root, field) = RB_BLACK;             \
	}

#define RB_GENERATE_REMOVE_COLOR(name, type, field, attr)                            \
	attr void                                                                        \
	name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
	{                                                                                \
		struct type *tmp;                                                            \
		while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&                  \
			   elm != RB_ROOT(head))                                                 \
		{                                                                            \
			if (RB_LEFT(parent, field) == elm)                                       \
			{                                                                        \
				tmp = RB_RIGHT(parent, field);                                       \
				if (RB_COLOR(tmp, field) == RB_RED)                                  \
				{                                                                    \
					RB_SET_BLACKRED(tmp, parent, field);                             \
					RB_ROTATE_LEFT(head, parent, tmp, field);                        \
					tmp = RB_RIGHT(parent, field);                                   \
				}                                                                    \
				if ((RB_LEFT(tmp, field) == NULL ||                                  \
					 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&            \
					(RB_RIGHT(tmp, field) == NULL ||                                 \
					 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK))             \
				{                                                                    \
					RB_COLOR(tmp, field) = RB_RED;                                   \
					elm = parent;                                                    \
					parent = RB_PARENT(elm, field);                                  \
				}                                                                    \
				else                                                                 \
				{                                                                    \
					if (RB_RIGHT(tmp, field) == NULL ||                              \
						RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)           \
					{                                                                \
						struct type *oleft;                                          \
						if ((oleft = RB_LEFT(tmp, field)) != NULL)                   \
							RB_COLOR(oleft, field) = RB_BLACK;                       \
						RB_COLOR(tmp, field) = RB_RED;                               \
						RB_ROTATE_RIGHT(head, tmp, oleft, field);                    \
						tmp = RB_RIGHT(parent, field);                               \
					}                                                                \
					RB_COLOR(tmp, field) = RB_COLOR(parent, field);                  \
					RB_COLOR(parent, field) = RB_BLACK;                              \
					if (RB_RIGHT(tmp, field))                                        \
						RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;            \
					RB_ROTATE_LEFT(head, parent, tmp, field);                        \
					elm = RB_ROOT(head);                                             \
					break;                                                           \
				}                                                                    \
			}                                                                        \
			else                                                                     \
			{                                                                        \
				tmp = RB_LEFT(parent, field);                                        \
				if (RB_COLOR(tmp, field) == RB_RED)                                  \
				{                                                                    \
					RB_SET_BLACKRED(tmp, parent, field);                             \
					RB_ROTATE_RIGHT(head, parent, tmp, field);                       \
					tmp = RB_LEFT(parent, field);                                    \
				}                                                                    \
				if ((RB_LEFT(tmp, field) == NULL ||                                  \
					 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&            \
					(RB_RIGHT(tmp, field) == NULL ||                                 \
					 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK))             \
				{                                                                    \
					RB_COLOR(tmp, field) = RB_RED;                                   \
					elm = parent;                                                    \
					parent = RB_PARENT(elm, field);                                  \
				}                                                                    \
				else                                                                 \
				{                                                                    \
					if (RB_LEFT(tmp, field) == NULL ||                               \
						RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK)            \
					{                                                                \
						struct type *oright;                                         \
						if ((oright = RB_RIGHT(tmp, field)) != NULL)                 \
							RB_COLOR(oright, field) = RB_BLACK;                      \
						RB_COLOR(tmp, field) = RB_RED;                               \
						RB_ROTATE_LEFT(head, tmp, oright, field);                    \
						tmp = RB_LEFT(parent, field);                                \
					}                                                                \
					RB_COLOR(tmp, field) = RB_COLOR(parent, field);                  \
					RB_COLOR(parent, field) = RB_BLACK;                              \
					if (RB_LEFT(tmp, field))                                         \
						RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;             \
					RB_ROTATE_RIGHT(head, parent, tmp, field);                       \
					elm = RB_ROOT(head);                                             \
					break;                                                           \
				}                                                                    \
			}                                                                        \
		}                                                                            \
		if (elm)                                                                     \
			RB_COLOR(elm, field) = RB_BLACK;                                         \
	}

#define RB_GENERATE_REMOVE(name, type, field, attr)                \
	attr struct type *                                             \
	name##_RB_REMOVE(struct name *head, struct type *elm)          \
	{                                                              \
		struct type *child, *parent, *old = elm;                   \
		int color;                                                 \
		if (RB_LEFT(elm, field) == NULL)                           \
			child = RB_RIGHT(elm, field);                          \
		else if (RB_RIGHT(elm, field) == NULL)                     \
			child = RB_LEFT(elm, field);                           \
		else                                                       \
		{                                                          \
			struct type *left;                                     \
			elm = RB_RIGHT(elm, field);                            \
			while ((left = RB_LEFT(elm, field)) != NULL)           \
				elm = left;                                        \
			child = RB_RIGHT(elm, field);                          \
			parent = RB_PARENT(elm, field);                        \
			color = RB_COLOR(elm, field);                          \
			if (child)                                             \
				RB_PARENT(child, field) = parent;                  \
			if (parent)                                            \
			{                                                      \
				if (RB_LEFT(parent, field) == elm)                 \
					RB_LEFT(parent, field) = child;                \
				else                                               \
					RB_RIGHT(parent, field) = child;               \
				RB_AUGMENT(parent);                                \
			}                                                      \
			else                                                   \
				RB_ROOT(head) = child;                             \
			if (RB_PARENT(elm, field) == old)                      \
				parent = elm;                                      \
			(elm)->field = (old)->field;                           \
			if (RB_PARENT(old, field))                             \
			{                                                      \
				if (RB_LEFT(RB_PARENT(old, field), field) == old)  \
					RB_LEFT(RB_PARENT(old, field), field) = elm;   \
				else                                               \
					RB_RIGHT(RB_PARENT(old, field), field) = elm;  \
				RB_AUGMENT(RB_PARENT(old, field));                 \
			}                                                      \
			else                                                   \
				RB_ROOT(head) = elm;                               \
			RB_PARENT(RB_LEFT(old, field), field) = elm;           \
			if (RB_RIGHT(old, field))                              \
				RB_PARENT(RB_RIGHT(old, field), field) = elm;      \
			if (parent)                                            \
			{                                                      \
				left = parent;                                     \
				do                                                 \
				{                                                  \
					RB_AUGMENT(left);                              \
				} while ((left = RB_PARENT(left, field)) != NULL); \
			}                                                      \
			goto color;                                            \
		}                                                          \
		parent = RB_PARENT(elm, field);                            \
		color = RB_COLOR(elm, field);                              \
		if (child)                                                 \
			RB_PARENT(child, field) = parent;                      \
		if (parent)                                                \
		{                                                          \
			if (RB_LEFT(parent, field) == elm)                     \
				RB_LEFT(parent, field) = child;                    \
			else                                                   \
				RB_RIGHT(parent, field) = child;                   \
			RB_AUGMENT(parent);                                    \
		}                                                          \
		else                                                       \
			RB_ROOT(head) = child;                                 \
	color:                                                         \
		if (color == RB_BLACK)                                     \
			name##_RB_REMOVE_COLOR(head, parent, child);           \
		return (old);                                              \
	}

#define RB_GENERATE_INSERT(name, type, field, cmp, attr)  \
	/* Inserts a node into the RB tree */                 \
	attr struct type *                                    \
	name##_RB_INSERT(struct name *head, struct type *elm) \
	{                                                     \
		struct type *tmp;                                 \
		struct type *parent = NULL;                       \
		int comp = 0;                                     \
		tmp = RB_ROOT(head);                              \
		while (tmp)                                       \
		{                                                 \
			parent = tmp;                                 \
			comp = (cmp)(elm, parent);                    \
			if (comp < 0)                                 \
				tmp = RB_LEFT(tmp, field);                \
			else if (comp > 0)                            \
				tmp = RB_RIGHT(tmp, field);               \
			else                                          \
				return (tmp);                             \
		}                                                 \
		RB_SET(elm, parent, field);                       \
		if (parent != NULL)                               \
		{                                                 \
			if (comp < 0)                                 \
				RB_LEFT(parent, field) = elm;             \
			else                                          \
				RB_RIGHT(parent, field) = elm;            \
			RB_AUGMENT(parent);                           \
		}                                                 \
		else                                              \
			RB_ROOT(head) = elm;                          \
		name##_RB_INSERT_COLOR(head, elm);                \
		return (NULL);                                    \
	}

#define RB_GENERATE_FIND(name, type, field, cmp, attr)  \
	/* Finds the node with the same key as elm */       \
	attr struct type *                                  \
	name##_RB_FIND(struct name *head, struct type *elm) \
	{                                                   \
		struct type *tmp = RB_ROOT(head);               \
		int comp;                                       \
		while (tmp)                                     \
		{                                               \
			comp = cmp(elm, tmp);                       \
			if (comp < 0)                               \
				tmp = RB_LEFT(tmp, field);              \
			else if (comp > 0)                          \
				tmp = RB_RIGHT(tmp, field);             \
			else                                        \
				return (tmp);                           \
		}                                               \
		return (NULL);                                  \
	}

#define RB_GENERATE_NFIND(name, type, field, cmp, attr)                \
	/* Finds the first node greater than or equal to the search key */ \
	attr struct type *                                                 \
	name##_RB_NFIND(struct name *head, struct type *elm)               \
	{                                                                  \
		struct type *tmp = RB_ROOT(head);                              \
		struct type *res = NULL;                                       \
		int comp;                                                      \
		while (tmp)                                                    \
		{                                                              \
			comp = cmp(elm, tmp);                                      \
			if (comp < 0)                                              \
			{                                                          \
				res = tmp;                                             \
				tmp = RB_LEFT(tmp, field);                             \
			}                                                          \
			else if (comp > 0)                                         \
				tmp = RB_RIGHT(tmp, field);                            \
			else                                                       \
				return (tmp);                                          \
		}                                                              \
		return (res);                                                  \
	}

#define RB_GENERATE_NEXT(name, type, field, attr)                       \
	/* ARGSUSED */                                                      \
	attr struct type *                                                  \
	name##_RB_NEXT(struct type *elm)                                    \
	{                                                                   \
		if (RB_RIGHT(elm, field))                                       \
		{                                                               \
			elm = RB_RIGHT(elm, field);                                 \
			while (RB_LEFT(elm, field))                                 \
				elm = RB_LEFT(elm, field);                              \
		}                                                               \
		else                                                            \
		{                                                               \
			if (RB_PARENT(elm, field) &&                                \
				(elm == RB_LEFT(RB_PARENT(elm, field), field)))         \
				elm = RB_PARENT(elm, field);                            \
			else                                                        \
			{                                                           \
				while (RB_PARENT(elm, field) &&                         \
					   (elm == RB_RIGHT(RB_PARENT(elm, field), field))) \
					elm = RB_PARENT(elm, field);                        \
				elm = RB_PARENT(elm, field);                            \
			}                                                           \
		}                                                               \
		return (elm);                                                   \
	}

#define RB_GENERATE_PREV(name, type, field, attr)                      \
	/* ARGSUSED */                                                     \
	attr struct type *                                                 \
	name##_RB_PREV(struct type *elm)                                   \
	{                                                                  \
		if (RB_LEFT(elm, field))                                       \
		{                                                              \
			elm = RB_LEFT(elm, field);                                 \
			while (RB_RIGHT(elm, field))                               \
				elm = RB_RIGHT(elm, field);                            \
		}                                                              \
		else                                                           \
		{                                                              \
			if (RB_PARENT(elm, field) &&                               \
				(elm == RB_RIGHT(RB_PARENT(elm, field), field)))       \
				elm = RB_PARENT(elm, field);                           \
			else                                                       \
			{                                                          \
				while (RB_PARENT(elm, field) &&                        \
					   (elm == RB_LEFT(RB_PARENT(elm, field), field))) \
					elm = RB_PARENT(elm, field);                       \
				elm = RB_PARENT(elm, field);                           \
			}                                                          \
		}                                                              \
		return (elm);                                                  \
	}

#define RB_GENERATE_MINMAX(name, type, field, attr) \
	attr struct type *                              \
	name##_RB_MINMAX(struct name *head, int val)    \
	{                                               \
		struct type *tmp = RB_ROOT(head);           \
		struct type *parent = NULL;                 \
		while (tmp)                                 \
		{                                           \
			parent = tmp;                           \
			if (val < 0)                            \
				tmp = RB_LEFT(tmp, field);          \
			else                                    \
				tmp = RB_RIGHT(tmp, field);         \
		}                                           \
		return (parent);                            \
	}

#define RB_NEGINF -1
#define RB_INF 1

#define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
#define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
#define RB_FIND(name, x, y) name##_RB_FIND(x, y)
#define RB_NFIND(name, x, y) name##_RB_NFIND(x, y)
#define RB_NEXT(name, x, y) name##_RB_NEXT(y)
#define RB_PREV(name, x, y) name##_RB_PREV(y)
#define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF)
#define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF)

#define RB_FOREACH(x, name, head)  \
	for ((x) = RB_MIN(name, head); \
		 (x) != NULL;              \
		 (x) = name##_RB_NEXT(x))

#define RB_FOREACH_FROM(x, name, y)                               \
	for ((x) = (y);                                               \
		 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
		 (x) = (y))

#define RB_FOREACH_SAFE(x, name, head, y)                         \
	for ((x) = RB_MIN(name, head);                                \
		 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
		 (x) = (y))

#define RB_FOREACH_REVERSE(x, name, head) \
	for ((x) = RB_MAX(name, head);        \
		 (x) != NULL;                     \
		 (x) = name##_RB_PREV(x))

#define RB_FOREACH_REVERSE_FROM(x, name, y)                       \
	for ((x) = (y);                                               \
		 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
		 (x) = (y))

#define RB_FOREACH_REVERSE_SAFE(x, name, head, y)                 \
	for ((x) = RB_MAX(name, head);                                \
		 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
		 (x) = (y))

#ifdef __cplusplus
}
#endif

#endif /* _SYS_TREE_H_ */
